in triangle ABC, sides are 'a' units as AD is perpendicular to BC , then in triangle ABD , AB2 = AD2 + BD2 a2 = AD2 + (a/2)2 [ since AD is perpendicular to BC ] a2 - a2/4 =AD2 = 3a2 /4 = AD2 ..........(1) in triangle ADC, AC2 = AD2 + CD2 a2 = AD2 + (a/4)2 3a2/4 = AD2 .........(2) from equation 1 and 2 3 a2 /4 = AD2 3 a2 = 4 AD2 3 AB2 = 4AD2 [since AB = a ]

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